Coupling network



Dec. 28, 1943.

H. w. `Bours.

coPLING NETWORK Fileduarch 1s, 1942 '2 Sheets-Sheet 2 @www Patented Dee. 28 ,v

y .UNITED STATES PATENT L 2,337,965 CoUPmNGNErwoltxr. Hendrik W. Bode, New York, N. Y., assigner to I 4 K I -Bell Telephone laboratories,

Incorporated,

New York, N. Y., a corporation of New York Application March 1s, 1942, semis. 435,111 v 7 claims. (ci. 11a- 44) )This invention relates to wave transmission networks and more particularly to networks for coupling a transmission line to a terminal device or load having la diierent impedance characteristic. yIts objects are to diminish wave reilections in a transmission line terminated by' a load having an impedance characteristic different from that of the 1ine;`to simplify the `equalization of the line-attenuation; and to improve the operation of transmission systems in which reactance networks-are employed for the equall zation o1 the line attenuation.

The networks of the invention have' the prop-v erty of minimum `transmission loss consistent with the requirement of physical. realizability.

, This minimum lossis equal to three decibels and It is approxiv is uniform at all frequencies,

mately half the loss encountered in impedance correcting networks of types heretofore used.l

It has been found advantageous in certain types of repeatered transmission systems to:

equalize the line attenuation by means ofy pure reactance networks, such as .resonant circuits," v connected `directly to the input and output terminals of the repeater ampliers. The advantage -in the use of such equalizers arises from the fact that, 'since they contain nojresistance ele- 'i ments, they do not introduce any noise into the system and, therefore, do notlimit the amount of amplification that can be used in the repeaters. 'Iheir use, however, entails a substantial amount of wave reflection at the line terminals,

.since the Vreactive impedances can -absorb no wave energy. The reflected waves in their passage along -the line have been found, under l certain conditions, to give rise to undesirable disturbances, such .as excessive cross-talk in adjacent circuits.y ,l

. lThe networks of the to be interposed between the line and the reactive equalizer and, when so connected, to preinvention are designedy of equalizers of this ltype' is described in my ear- ,I

sent to the line a resistive impedance equal to the: i resistive impedance of the line. At the Junction point to the equalizer'the impedance presented A to tlie,`e;|ua .lizerV is equal `to' the line impedance. Accordingly, thefconditionsunder which the 'equaliser functions are not y altered by them-'- sertion'fof the network. but vthewave .reflections back-into the `line are substantially suppressed.' 'l i 'In theraccomponying drawings,

Fig. 1 Vshows application of the invention intheinput circuitsef a telephone repeater;

Fig.. 2 ireiers to a detail of Fig. 1;'

and!l are diagrams illustrating Ithe Y the invention, and

ability ynickel-iron alloys of thenetworks of the invention.`

lratio equal to 1.\/2 from the primary, or line Figs. 5to 10 inclusive,'show additionalforms` v ff In Fig. 1, the coupling network of .the inven.- tion is shown in one of itsforms at I0 coupling f a transmission line Il with areactive` equalizing` network I2 in the input circuit of ayfeedbackl amplifier i3.: The showing is representative vof the input side of a repeater vin a multiplex carrier telephone' system using -high frequency carriers. The line Il may be anopen'wire line, a

cable, or a coaxial conductor J line, itsv impedance at the 'operating frequencies beingv a substantially pure resistance of constant value;` The equalizing network, which in the form illustrated comprises a. .tuned transformer ,IL/a sl'eries antiresonant circuit .IB and a shunt ca-f pacity I6, is vso designed as to'produce at its out.- put terminals is, ta' a voltagewhich increases. with frequency in. such manner as` to compensate fthe attenuation in the line. The 'design'.

lier United States Patent' No.2,24 2,878, issued? y May 20, 1941, wherein it is pointed out that the logarithm of the effective resistance measured at terminals ta, ta' when thel equalize'ris connected to the .line should have the same fre-V quency variation as the attenuation in the line.

The ilrst. stage only of the repeater ai'rlpllerv l) is shown together with the feedback impedance Zr, the feedback being of the series type. The l input impedanceof the first ampliier tube is. indicated by the capacity C which represents the electrode capacity and such" other parasitic capacities as are effective between the control grid and the cathode. This capacity isl ordinarily small and its effective impedance is greatly mull ,tiplied by the feedback action.: Consequently, the impedance into which the equalizer works maybe regarded as infinite' or open circuit in so far as it affects the voltage developedfat the output terminals t3, t3', fr

The coupling network I0 comprises two. transe formers I1 and il, the two primary windings/1j and the' two secondary windings of which are connected in series. lThese transformers-should and should be designed so 4that throughout the operating frequency range theybehave substantially like Aideal transformers. f For this purv pose the useofmagnetic 'cores of. high permeis advantageous. A... r Transformer I1 has a .voltagetransforxnation side, to thesecondary and transfin'xner, I8 has a voltage transformation 'of the reciprocal value Vzl. Shunt'ed across the secondary put impedance, Z, `ofequalizer i2 measured at terminals t2, t2'. The form of this inverse imj '-pedance and the'values'of its elements can be derived from' the known input impedance of the equalizer by well-known principles. A configu ration suitable iorgthe particular system illustrated in Fig. l is shown in Fig. 2.

When they elements have the Values given above, the coupling network i has these properties: When terminated by the equalizer i2 it presents to the line a matching impedance equal toRo; when terminated by the line it presents to the equalizer a constant resistive impedance equal 'to Ro; and .its inclusion between the line and the equalizer reduces the voltage at the equalizer output terminals by a constant amount equal to three decibels at all frequencies. lukewise, if the equalizer and the coupling network are located in the output circuit of a high mpedance amplifier, the currentI delivered to the line is reduced uniformly by three decibels because of the inclusion of the network. This loss is the minimum uniform loss that can be achieved with a physically realizable network.

The networks of the invention may taire various forms other than that shown in Fig. 1, certain of which will be described later. All have the properties described above and all have certain characteristic featuresin common. These characteristic features are developed in the following analysis of the principles underlying the operation of the invention.

It is convenient to begin the analysis by establishing ythe three-decibel loss as the theoreti- .cal minimum for an impedance matching network coupling a. resistivel source, represented by the-line, to a reactive load, represented by the equalizer. This may` be done most simply by considering the converse problem of the delivery of power to the line from a current source having ininitel impedance connected to the terminals of the equalizer. This `condition is illustrated in Fig. 3 in which the complete system is shown reduced to its simplest schematic form. The line is represented by its resistive impedance Rc and the remainder of the circuit isreplaced by its equivalent T-network comprising impedance Zi, Zn and Za. The symbols R1, Rz, etc. and X1, Xa, etc. will be used to represent the real and imaginary components ofthe Zs with the corresponding subscripts. A current I is assumed to be delivered. to the circuit at terminals ta, ta and to appear in the line with a value Io. v

The powerdelivered to the circuit and the power which reaches the line are equal to UFR. and IIoIZRn, respectively, Re denoting the resistance component of the total impedance opposed to the lcurrent I. 'If 'the reactive equalizer matching, absorb some power and the ratio of the two powers Vdeined'above then becomes a measure ofthe loss penalty incurred in effecting an impedance match to the line. From the geometry of the circuit to be givenby Since Z1, Zz and Zaare merely thebranches of the equivalent T ofthe actual circuit, it is not necessary that all of their resistance components R1, R2 and Re be positive for the circuit' as a whole to be physicallyrealizable. If, for exam ple, R3 l.could bemade sufllciently negative, it would be possible to make the power ratio as favorable las desired and even to convert it to a gain. It is known from general network theory, however, that a four-terminal network is physically realizable as a passive structure only .if the determinant of the matrix of the real parts of 'the open circuit driving point and transfer innl pedances is positive at every frequency. As applied to the T-network of Fig. 3, this condition is equivalent to l x R1R3+R2R3+ RgRl The limiting case in which the condition isjust met so that the equality sign inV Equation 2 applies is obviously the most favorable one. Assuming this limiting case and using Equation 2 'to eliminate Ra, Equation I becomes `Power rat1o1+Ro Rl+ 2) (Rs, X22) (3) The further requirement that the line impedance befmatched by the network may now be introduced. Since the circuitA is assumed to open at terminals ta, t3', this requirement is simply that When these relations are introduced the righthand side of Equation 3 becomes numerically equal to two. Thus-when the limiting condition of physical realizability is just met and the net- 'work matches the line impedance, exactly half of the power applied to the circuit reaches the line. This corresponds to a loss of three decibels and represents the minimum obtainable. Since the reactive equalizer, which was included in the T-network of Fig. 3, can absorb no power, all of the power loss must occur vin the coupling network. The limiting condition of physical realizability set forth in Equation 2 therefore applies to the'coupling network per se in its function of coupling the resistive line to the finite reactive terminal impedance provided by the equalizer.

The minimum loss condition hasbeen discussed above in connection with a circuit in which power is supplied to aline from a sourcehaving innnite impedance. This is representative of the output circuit of a high impedance amplifier, for example, one using high impedance pentode tubes; The analysis may be extended to an input circuit'such as shown in Fig. 1 by the principle of reciprocity. Inthat case the complete termination comprising the coupling network and the equalizer together when subject to the realizability condition may be regarded as one providing the maximum output voltage consistent with impedance matching.

The general characteristics of the coupling network may now be considered. In Fig. 4 the cou- ;this ratiomay be shown applied to the coupling network itselfbecomes tine algebra.44 They are given by and 'k 'ingtherequired system 'of 'impedanceal One of kthese is illustrated in Fig. 1. ,Qthers are SllOlWll#v l nais tntz'is represented by Z. For the determination of Z., Zb and Ze the coupling network may bev specified by threerequirements.v The first is the requirement that the impedance presented to the line should equal the line resistance Ro when the structure is terminated at its other end by theequalizer impedance Z.. The second is the requirements of minimum vloss,y which when where R., Rs and Re denote the resistance parts o f Z., Zu and Ze. The third is that the impedance presented to the equalizer shallalso equal Ro. which is desirable in'order that the gain charac'- teristic produced by the equalizer may be independent of the presence or absence of the cou pling network. l

4By this choice of the requirements, particularly the third, I have been able 'to devise various network structures in which the performance is substantially independent of frequency. That is, the impedance matching and the achievement of minimum loss obtain through a very wide range limited only by theimperfections of the transformers. The values of the branch impedances can be obtained from the specified requirements by rou- The paling of the transformer windingsis not v. lmaterial in the networks of Figs. 1, 5 and 6.

In Figs'. 7 to, 10, the arrows -indicate windings l that should be Wound in the same direction on the clore.` The network of Fig. 10 may be derived from the network shown in'Fig. 8 by substituting a single windingtappedat its mid-point for the two primary windings. A Y .l

The open circuit driving point and transfer impedances 'can be' computed foreach of the net- ,works by well-known'methodsof network analf-- v ysis. It is to be observed that in each network two impedance transformations of different mag-f" nitudes are involved. The circuit configurations i and the magnitudes of thetransformation ratios are so chosen that the value of the resistance is subject to a step-up of two toone from the line terminalsto thel output terminals, while the value of the reactive impedance4 is decreased in the same ratio.v

To the extent that `the various transformers act like ideal transformers, al1 of the coupling atv their output terminals land have 'open circuit networks ,of the invention have cpexrfcircuit driv-A ing point impedances substantially equal to4 R 2 i at theirline terminals and to transfer impedances equal` to i s @(RUJFZL Departures from these values may be caused by low'lmpedance of the transformer windings or by imperfect coupling of the windings. How- In terms of its open circuit driving point and Y.

in which the upperfleft-hand "term` lower rightehand term'denote i the open circuit drivingv ever. with the high eiiiciency transformers that are 'now available, the errors arising fromI thesey causes are usually negligible over a, very lwide 'frequency range.

What is claimed is:

1. Means for coupling aline of resistive impedance'Rty to a'load having a prescribed' frequency dependent reactive impedance Z with minimum .attenuation and With impedance matching- `at the line terminals throughout a point impedances at the line andv equalizer terj minals respectively and the otherI two terms del' valuesmay be readily verified from the values of vratios I have been able tc devise structures hat' `m Figs. s to 1c, the values y I 'andthe reactive'impedances are indicated in the drawings in terms ofthe line resistance-and the reactance of the equalizer. The voltage ratios.

,..of the various-'transformers are also given.

ywide frequency range. comprising a four-terminal network having open circuit driving point impedances lat its line and load terminalssubstanwiesiectively, and an open circuit transfer imped- 'Y -note the open circuittransier impdance. y'l'.'hese ancez'substantially equal to 1 said rietworkincluding'a resistor, a reactor having-fan* impedance inversely related. to Z, and .transforming ymeans whereby. the effective imvparlantes 'of'said resistor and saidreactor meas-` v,ur-ed at the network terminals are subject to reciprocally related transformations.

L12." A foureterminal'network for coupling a line cf resistiveimpedance Ro to a load having va prei scribed frequency dependent reactivev impedance of value Z with minimum attenuation and with impedance matchingv at the linev terminals throughout a. wide frequency-range, comprising a resistor, a reactive impedance inversely related to the prescribed impedance Z, and a plurality of transformer means having diierent transformation ratios coupling said resistor and said inverse impedance, to the input and output terminals of the network, the impedances of the said network elements and theytransformation ratios of said transformer means being proportioned to make the open circuit driving point impedances ofthe network at the line and load i terminals substantially equal to respectively, and to make the open circuit trans fer impedance substantially equal to terminals of the network, the connections of the said transformer means being so arranged that the impedancesof said resistor and said inverse' impedance are subject to reciprocally related impedancetrans'formations .between the line and load terminals of the network, and the network elements being proportioned to make the open circuit transfer and driving point impedances atl the line and load terminals substantially equal to respectively, at all frequencies'in a wide range.

4. A four-terminal coupling network for cou pling a line of resistive impedance Ro toa termi;- nal device having a prescribed frequency dependent reactive impedance of value Z comprising a pair of transformers having their primary windings connected in series between the line terminals of the network and having their secondary windings connected in series between the other terminals of the network, one of'said transformers having a voltage transformation ratioof 1 :V

between its primary and secondary terminals and the' other transformer hav i ng a corresponding transformation ratio oi\/2:1, a resistor connected across one winding of the said one trans- 5 former, and a reactive impedance inversely related to the prescribed impedance Z connected across a winding of said other transformer, said resistor and said inverse impedance being proportioned to make the open circuit impedance of ,10 the network at the line terminals equal to- 5. A coupling network lin accordance with claim i in which the resistor is connectedacross the second Winding of the said one transformer andhas a resistance 2Ro and in which the inverse impedance is connected across the secondary winding of the said other transformer and 2@ has a impedance equal to v En.

k6. A network for coupling a line of resistive impedance Reto a terminal device having a reactive impedance of value Z 'comprising transformer means having a secondary winding ar-l ranged i'or connection to said Vterminal device, a first primary winding and a second primary 3U, winding, said windings having turns in the ra tios \/2:l:2, respectively, areactive impedance of `value 2Z connected in series with said-first primary winding,l a resistance of value Ro connected in series with said second primary winding, a pair of input terminals for connection to the line, and circuitsrconnectingsaid primary windings andtheir.

m respectively associated tween said terminals. n

7. A network for coupling a line of resistive impedance Ro to a terminal device having areactive impedance of value Z comprising a transformer having a secondary winding arranged for connection to said-terminal device and a centrally tapped primary winding, the two portions of vsaid primary winding and said secon d ary winding having turns in the ratios 1:1:\/2, a pair of input terminals for connection to the line, a resistance of value 'Rnconnected between one oi' said terminals and one end of said primary winding, a reactive impedance of value connected between said one terminal and the center tap of said primaryvwinding and a connection impedancesin parallel be- @o from the other of said-terminals to the other end of said primary Winding.

' Y' -HEND RIKW.BODE. 

